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Hubbard, R Glenn;Skiooer, Jonathan;Zeldes, Stephen P

The American Economic Review ; May 1994; 84, 2; ProQuest Central pg. 174

WHY DO PEOPLE SAVE?t

Expanding the Life-Cycle Model: Precautionary Saving and Public Policy

By R. GLENN HUBBARD, JONATHAN SKINNER, AND STEPHEN P. ZELDES*

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VOL. 84 NO. 2 WHY DO PEOPLE SAVE? 175

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the stochastic processes using available cross-section and panel data sets on house­ holds. In addition, we include asset-based means-tested public welfare programs (e.g., Aid to Families with Dependent Children, Food Stamps, Supplemental Security In­ come, and Medicaid). In this research pro­ gram, we are looking at how close a model with rational optimizing consumers can come to matching a wide range of empirical facts about consumption and wealth. 1

The improvements to the life-cycle model under certainty or perfect markets come in three forms. First, adding uncertainty, even in cases where it does not change the opti­ mal decision rule for saving, introduces het­ erogeneity in wealth and saving when households differ in the realizations of seri­ ally correlated earnings and health ex­ penses. Second, we assume household pref­ erences that do not generate "certainty equivalence," so that the introduction of uncertainty changes household decision rules in important ways. Third, many house­ holds face a high implicit tax on saving should they become eligible for AFDC, Medicaid, or Food Stamps. These social insurance programs with asset-based means-testing alter in significant ways the incentives to save.

In Hubbard et al. (1993), we show that the combination of these factors can explain much of the observed cross-sectional het­ erogeneity in wealth holdings in the 1984 Panel Study of Income Dynamics (PSID), including the presence of a substantial num­ ber of households with low levels of assets at retirement. In this paper, we follow up on these households; we use data from the 1989 PSID to examine transitions in wealth holdings between 1984 and 1989. Our model

1In Hubbard et al. (1994), we show that, using realistic parameter values, our model replicates empiri­ cal regularities in (i) aggregate wealth and the aggre­ gate saving rate, (ii) cross-sectional differences in con­ sumption-age profiles by lifetime-income group, and

(iii) short-run time-series properties of consumption and income. In Hubbard et al. (1993), we analyze the effects of a social insurance program with asset-based means testing and show that our model helps explain the observed cross-sectional distribution of wealth.

implies that in many cases saving rates will be low among those with low initial levels of wealth (i.e., that low wealth may be an "absorbing state" over a lengthy period of time). We find that this is consistent with evidence from the PSID. More broadly, the results of our 1993 and 1994 papers indicate that our model can explain the saving be­ havior of "savers" and "nonsavers" alike.

I. Life-Cycle Models of Saving Decisions

We begin by presenting a simple descrip­ tion of our general multiperiod model with multiple sources of uncertainty (readers in­ terested in a more comprehensive descrip­ tion should see our 1994 paper). Consumers maximize expected lifetime utility, given all of the relevant constraints. At each age t , the consumption chosen maximizes

T

(1) E, L, Dp( Cs) / ( 1+ 5 ) s -t

subject to the transition equation

(2) As = As _ 1( l + r )

+ Es + TRs - Ms - Cs

plus the additional constraints that

(3) As O V s.

The first expression describes the opti­ mization in which consumption excluding medical expenses, C,, is selected to maxi­ mize expected lifetime utility (where E is the expectations operator conditional on in­ formation at time t ), discounted based on a rate of time preference 5. To allow for a random date of death, Ds is a state variable equal to unity if the individual is alive and zero otherwise, and T is the maximum pos­ sible length of life. The household begins

1

period s with assets from the previous pe­ riod plus accumulated interest, As _ 1(1 + r ), where r is the nonstochastic real after-tax rate of return. It then receives exogenous

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earnings Es , pays out necessary medical ex­ penses Ms, and receives government trans­ fers TRs. It is left with

(4) Xs = As -1( l + r ) + Es - Ms + TR.

which, following Angus Deaton (1991), we denote as "cash on hand."

Given Xs, consumption is chosen, and what remains equals end-of-period assets, A•. We assume that no utility is derived from medical expenditures, as these costs only offset the damage inflicted by ill health. The borrowing and terminal constraints in equation (3) prevent negative assets in any period. Since the setup includes a govern­ ment-guaranteed level of consumption, bor­ rowing constraints rule out borrowing in one period, defaulting, and receiving the guaranteed consumption in the subsequent period.

For simplicity, we specify a generic trans­ fers function including income-based and asset-based means testing, as well as pay­ ments tied to medical expenses:

(5) TR.= max[O, (C + M.)

-( A 5 _ 1( l + r ) + E.)] .

The mm1mum level of consm,!!ption guar­ anteed by the government is C (the "con­ sumption floor"). Transfers equal this con­ sumption floor plus medical expenses minus all available resources (if that amount is positive, and zero otherwise). Simply put, transfer payments guarantee a minimum standard of living after medical expenses equal to C. The one-for-one reduction in transfer payments in response to increases in assets or current earnings captures in a stylized fashion the penalty on saving of asset-based means-tested programs. Be­ cause eligibility is conditional on having as­ sets less than some specified amount, such programs place an implicit tax rate of 100 percent on assets above the limit. We dis­ cuss these incentives in greater detail in our 1993 paper.

Given our interest in individual as well as aggregate saving, we allow for heterogeneity in life-cycle saving decisions across different lifetime-income groups. Using educational attainment as a proxy for lifetime income, we specify three groups: households whose head does not have a high-school degree, households whose head is a high-school graduate, and households whose head has a college degree.

Solving the model requires a functional form to describe household utility, an em­ pirical characterization of the sources of uncertainty, a description of the consump­ tion floor, and assumptions regarding the rate of time preference and real interest rate. We assume that the period utility function is isoelastic, and we experiment with alternative values for both the coeffi­ cient of relative risk aversion and the rate of time preference. Mortality probabilities are taken from official data. We estimate func­ tions for earnings (and Social Security and private pension receipts) and out-of-pocket medical expenses using micro data. Residu­ als from log-earnings and log-medical­ expenses regressions are used to estimate education-group-specific AR(l) processes to account for exposure to risk of fluctuations in earnings and medical expenses. We esti­ mate a consumption floor of $7,000 in 1984 dollars. We solve numerically the dynamic­ programming problem; this yields the opti­ mal state-contingent consumption function.

In what follows, we will compare our re­ sults to those from an alternative approach in the same spirit that also examines the effects of uncertainty on optimal intertem­ poral consumption decisions. Deaton (1991) and Christopher Carroll (1992) reconcile the life-cycle model's predictions with the em­ pirical finding of low levels of wealth accu­ mulation by many households by assuming a high rate of time preference (relative to the real interest rate). In this case, absent un­ certainty, households would like to borrow against future income. With earnings uncer­ tainty (and in some cases borrowing con­ straints), households maintain a "buffer stock" or contingency fund against income downturn, but households' impatience keeps buffer stocks small.

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II. Why Don't People Save?

TABLE 1-TRANSITIONS BETWEEN ASSET CATEGORIES OVER A FIVE-YEAR PERIOD,

ACTUAL AND SIMULATED DATA

A central prediction of the life-cycle

framework is that households accumulate substantial assets for retirement. An impor­ tant empirical puzzle, however, is that many households have very low levels of accu­ mulated wealth over their life cycle. In Hubbard et al. (1993), we use 1984 data from the PSID to show that a significant fraction of households with low lifetime earnings (represented by educational attain­ ment) have preretirement wealth accumula­ tion much too small to be consistent with the perfect-markets version of the life-cycle model. However, households with higher lifetime earnings (as proxied by a college degree) exhibit saving behavior more consis­ tent with the predictions of the life-cycle model in the sense that most households have substantial assets near retirement.

In this section, we extend these results to consider what happened to these "low wealth" households in 1984 over the subse­ quent five years. The empirical evidence comes from the 1989 wave of the PSID, which asked detailed questions about wealth holdings similar to those in the 1984 survey. The simulated evidence comes from draw­ ing random shocks from the distributions of earnings and out-of-pocket medical ex­ penses, which, together with the optimal consumption function, are used to generate artificial "life histories" of consumption and wealth for a large number of simulated households. To contrast the predictions of our generalized life-cycle model with the "buffer-stock" alternative, we also generate simulated consumption, wealth, and earn­ ings panels using the assumption of a high time-preference rate (10 percent) and a very low consumption floor.

We analyze movements of household as­ sets between 1984 and 1989 for households headed by an individual aged 65 years or younger in 1984. We grouped assets into four classes according to whether the level of assets A is such that A $1,000;

$1,000 < A $5,000; $5,000 < A $25,000;

or A > $25,000 (all figures are in 1984 dol­ lars). The top entry in each cell in Table 1 reports the proportion of households with a

Final assets

Notes: The numbers reported above are the percent­ age of those households with given initial assets ending up after five years in the designated final asset bracket (each row, therefore, sums to 100). The top entry, in bold type, is calculated from the Panel Study of In­ come Dynamics using the 1984 and 1989 wealth sup­ plements. The middle entry is drawn from our simula­ tion model with uncertainty about lifespan, earnings, and out-of-pocket medical expenses, and a consump­ tion floor of $7,000. The bottom entry, in italics, comes from simulations of our uncertainty model with a rate of time preference equal to 10 percent and a $1 con­ sumption floor. All figures are in 1984 dollars.

given level of assets in 1984 with given levels of assets in 1989. These transition calcula­ tions reveal that, even over a five-year pe­ riod, there is substantial persistence of low wealth in households. For example, of those with less than $1,000 total wealth in 1984, 56 percent still had less than $1,000 total wealth in 1989.

The second entry in each cell of Table 1 is drawn from simulations of our model with uncertainty over lifespan, earnings, and out­ of-pocket medical expenses under the as­ sumptions that the annual rate of time pref­ erence and the interest rate are both

3 percent and the consumption floor is

$7,000. The transition matrix from the simu­ lated data matches the actual data quite closely. For example, 60 percent of simu­ lated households (compared to 56 percent

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of actual households) who initially hold less than $1,000 in assets still have less than

$1,000 in assets five years later. The simu­ lated transition probabilities at other levels of wealth also match the actual data reason­ ably well.

There are two reasons why our model implies a high degree of persistence in low wealth. First, the simulated earnings and medical expenses exhibit considerable per­ sistence (based on empirical parameters), so that a significant adverse shock to either of these two variables signals an adverse real­ ization in the future and generates contin­ ued low consumption and low wealth. Pre­ liminary results using a certainty-equivalent life-cycle model (i.e., one in which the household recalculates optimal consump­ tion each period given the shocks to earn­ ings and medical expenses but makes deci­ sions as if all future variables were known with certainty) suggests that, even near re­ tirement, roughly one-tenth of the popula­ tion may exhibit low levels of wealth be­ cause of bad earnings or health shocks.

The second reason for the strong persis­ tence in low levels of wealth is the existence of asset-based means testing of welfare pro­ grams. Low wealth holdings are likely to be an "absorbing state," in the sense that low levels of wealth increase the likelihood of receiving the consumption floor; saving while receiving transfers is discouraged by the implicit tax associated with means test­ ing. By contrast, households with higher lev­ els of wealth are less likely to qualify for social insurance programs, so that saving is less discouraged for this group.

The third entry in each cell of Table 1 is drawn from simulations of a "buffer-stock" model with a time preference rate of 10 percent, interest rate equal to 3 percent, and a negligible consumption floor of just

$1. The buffer-stock model predicts much less persistence of low levels of wealth than experienced by households in the PSID. The intuition is that, in the buffer-stock model, wealth accumulation serves primarily to in­ sulate consumption against a bad draw in disposable income. Should a household ex­ perience low wealth because of an unusu­ ally bad draw, the household is careful to

rebuild the buffer stock. Under the buffer­ stock model, there are fewer than 7 percent of households with initial wealth less than

$1,000 in "1984" who still have low wealth five years later.

III. Conclusions and Implications for Public Policies Toward Saving

The perfect-markets version of the life­ cycle model has directly or indirectly con­ tributed much of our intuition about effects of public policies on household saving deci­ sions. While the findings of our research project cast doubt on the applicability of the standard, perfect-certainty version of the life-cycle model for policy analysis, we con­ clude that a well-specified optimizing life­ cycle model with uninsured idiosyncratic risks and social insurance can explain many empirical observations, including the saving behavior of much of the population. It is therefore likely to be a useful tool for ana­ lyzing the effects of government policy on saving behavior. We briefly consider two examples below.

In the traditional perfect-markets version of the life-cycle model, the taxation of capi­ tal income has a significant impact on ag­ gregate saving. The policy implications stemming from such models-that con­ sumption taxes are more efficient than income taxes, for example-are largely predicted on the high interest elasticity of saving in the basic model. Recent research by others (see e.g., Eric Engen, 1993) has shown that, in a setting with uninsurable idiosyncratic risk, the after-tax rate of re­ turn exerts a smaller impact on saving. While this is a topic for future research, taking seriously uncertainty and imperfect insur­ ance and lending markets is likely to yield tax-policy implications quite different from conventional life-cycle models.

The failure of perfect-markets versions of the life-cycle model to explain the negligible wealth accumulation by many households, particularly those with low lifetime incomes, has stimulated interest in models of saving that can account for such behavior. Our approach has addressed this question and has emphasized that expenditure policy,

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such as the design of social insurance pro­ grams, may exert as large an effect on sav­ ing behavior as tax policy. The asset-based means testing of AFDC, Supplemental Se­ curity Income, and Medicaid may ultimately affect the consumption and saving choices of low-income households by more than even extreme variations in explicit marginal income tax rates. Raising the asset limit for AFDC and food stamps from below $3,000 to $10,000, a proposal put forth by Jack Kemp, the former Secretary of Housing and Urban Development, could increase saving among those least likely to save for retire­

Carroll, Christopher D. "The Buffer Stock Theory of Saving: Some Macroeconomic Evidence." Brookings Papers on Eco­ nomic Activity, 1992, (2), pp. 61-135.

Deaton, Angus. "Saving and Liquidity Con­ straints." Econometrica, September 1991,

59(5), pp. 1221-48.

Engen, Eric M. "Precautionary Saving and the Structure of Taxation." Mimeo, Uni­ versity of California-Los Angeles, 1993.

Hubbard, R. Glenn; Skinner, Jonathan and Zeldes, Stephen P. "Precautionary Saving and Social Insurance." Mimeo, University of Virginia, 1993.

ment. Whether the increased saving justifies . "The Importance of Precautionary

the revenue cost of the enhanced program is, of course, a question for future research.

REFERENCES

Auerbach, AJan J. and Kotlikoft', Laurence J. Dynamic fiscal policy. Cambridge: Cam­ bridge University Press, 1987.

Motives in Explaining Individual and Ag­ gregate Saving." Carnegie-Rochester Con­ ference Series on Public Policy, 1994 (forthcoming).

Thaler, Richard H. "Psychology and Savings Policies." American Economic Review, May 1994 ( Papers and Proceedings ), 84( 2),

pp. 186-92.